Multi-leg breeches calculator (3 to 6 legs)
Split one round pipe into 3 to 6 equal legs spaced evenly round a circle. Enter the main and leg diameter, number of legs, height and leg angle; you get one leg pattern to cut that many times.
Enter your measurements
Seam
4,858.3mm
Approximate, within ±2.0 mm
- Cut length
- In the app
- Sheet size
- In the app
Every result is in Trueflat
The free web version shows the main result and the drawing. Trueflat gives you every mark and measurement, and exports a cut sheet. It is free to download.
How to lay it out
Place the legs in plan
Draw the main pipe circle and a circle of radius H tan θ. Place the leg mouth centres evenly on it, 360° ÷ k apart.
Divide one leg
For one leg, divide its seat on the main pipe (360° ÷ k wide, on the outer side) into equal parts and the rest of the circle into equal parts. Divide its mouth at the same angles.
Mark the crotch points
Join matching points with generators. Mark where each crotch-side generator meets the plane shared with the nearer neighbour leg.
Triangulate the leg
Find true lengths of generators and diagonals and lay out the triangles from the outer seam line.
Cut k legs
Join the edges and cut the same pattern once per leg. Each crotch edge has a corner in the middle, where the two neighbour planes meet.
Good to know
- This pattern is approximate; the result card shows how close it is.
- Source: Derived from first principles: each leg is the oblique cone between the main-pipe circle and the leg mouth, the crotch lies in a plane, so every facet is flat and the leg is laid out by triangulation on the middle of the sheet. Checked against an independent reference implementation in Trueflat.
Method and formula
A multi-leg breeches divides one main pipe of diameter Dg into k equal legs of diameter d, with k from 3 to 6. The leg mouths sit on a circle of radius
- rc = H tan θ,
spaced 360° ÷ k apart, with θ the lean of each leg from the main pipe axis. Each leg is a slanting cone from the main pipe circle to its mouth. It meets each neighbour on a flat plane, so its crotch is made of two flat curves that meet at a corner in the middle. Each leg's seat on the main pipe is 360° ÷ k wide, centred on its outer side.
All legs are identical, so Trueflat draws one pattern and the totals count it k times. Because every facet is flat, the leg is triangulated without twist; the only error is drawing the curves with chords. The mouth is short by at most r(w³ + (π − w)³) ÷ (12n²), with w = π ÷ k.
Limits: θ from 15° to 50°, the range in which only neighbouring legs meet; neighbouring mouths must not overlap (2rc sin(π ÷ k) ≥ d); mouths at least 5 mm clear of the crotch planes. Inside or outside sizes are converted approximately and rejected above 1 mm of mouth deviation.
Worked example
Dg = 400 mm, d = 150 mm, 3 legs, H = 400 mm, θ = 25°, n = 4. The mouth circle radius is rc = 186.52 mm and each seat is 120° wide (w = 60°). The crotch corner sits 256.80 mm up, the mouths clear the crotch planes by 86.53 mm and the shortest generator is 151.11 mm. One leg has an area of 207 244.21 mm²; three legs need 621 732.63 mm² of sheet.
Questions
How is this different from a two-leg trouser piece?
A trouser piece has two legs and one crotch plane. Here 3 to 6 equal legs sit evenly round the main pipe, and each leg meets two neighbours, so its crotch edge has a corner in the middle. All legs share one pattern.
Why is the leg angle limited to 15°–50°?
The layout assumes each leg meets only its two neighbours. Trueflat has checked that this holds from 15° to 50°; outside that range it has not been checked, so the input is rejected.
Is the pattern exact?
Up to the chords used for the curves. With k legs each seat half-angle is w = π ÷ k, and the leg mouth is short by at most r(w³ + (π − w)³) ÷ (12n²). Each crotch corner falls on a division, so no error is added there.
Similar calculators
More in TrueflatConeTruncated coneCone by triangulationSee what the app does